CN110865344B - Rapid side lobe suppression method under pulse Doppler radar system - Google Patents

Rapid side lobe suppression method under pulse Doppler radar system Download PDF

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CN110865344B
CN110865344B CN201911159722.0A CN201911159722A CN110865344B CN 110865344 B CN110865344 B CN 110865344B CN 201911159722 A CN201911159722 A CN 201911159722A CN 110865344 B CN110865344 B CN 110865344B
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田静
张彪
吴嗣亮
崔嵬
宁晨
王烽宇
孔梓丞
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Abstract

The invention discloses a method for quickly inhibiting side lobes under a pulse Doppler radar system, which is used for solving the problem of high side lobes in the radar distance-Doppler imaging process, thereby obtaining accurate parameter estimation and obtaining a more ideal imaging effect; the invention provides a fast side lobe suppression method based on a two-dimensional matched filtering result, aiming at solving the problem of high side lobe of distance-Doppler after two-dimensional matched filtering in a pulse Doppler radar, wherein the method can realize side lobe suppression with lower calculation amount and improve the parameter estimation precision and imaging quality of a target in a multi-target scene by adding a processing window to the two-dimensional matched filtering result and utilizing an iterative adaptive method based on least square to realize side lobe suppression; due to the adoption of windowing processing, the covariance matrix is subjected to dimension reduction processing, the calculation complexity can be reduced, and the calculation amount is further reduced by utilizing the structural relationship among the matrixes.

Description

Rapid side lobe suppression method under pulse Doppler radar system
Technical Field
The invention belongs to the technical field of radar measurement, and particularly relates to a method for quickly inhibiting side lobes under a pulse Doppler radar system.
Background
In the pulse radar distance-Doppler imaging process, the traditional matched filtering algorithm has the problem of high side lobe, when the target distribution is close, a weak target is easily submerged in the side lobe of a strong target, and the parameter estimation effect and the imaging quality are influenced. In order to suppress the side lobe interference and further improve the imaging quality, in 2009 IEEE Transactions on Signal Processing 57, vol.3, page 1084 to page 1097, Li J et al in "Range-Doppler imaging via a train of combining pulses" propose a non-parametric iterative adaptive algorithm based on weighted least squares, which can suppress the Range-Doppler side lobe to the noise floor to obtain a high-quality Range-Doppler image. However, the huge calculation amount of the algorithm limits the application of the algorithm in a real-time system.
In order to reduce the calculation amount of the iterative adaptive algorithm, in the 2011 IEEE Transactions on Signal Processing 59, No. 9, No. 4154 to No. 4167, Glentis et al in the text "effective implementation of iterative adaptive estimation techniques", a fast algorithm based on Gohberg-Semencul decomposition and fast Fourier transform is proposed, which can reduce the calculation amount by about two orders, however, the algorithm needs a covariance matrix with a Toeplitz structure, and thus cannot be directly used in a radar system. In "IEEE Signal Processing Letters" 2011, volume 17, No. 4, pages 339 to 342, Andrea J et al, in the text "Coherence prediction from non-null structured sampled sequences", propose an iterative adaptive algorithm for data segmentation. The computational complexity is effectively reduced. There is a large performance penalty for this algorithm. Affecting the imaging quality of the radar.
Disclosure of Invention
In view of the above, the present invention provides a method for rapidly suppressing sidelobes in a pulse doppler radar system, so as to solve the problem of high sidelobes in a radar range-doppler imaging process, thereby obtaining accurate parameter estimation and obtaining a more ideal imaging effect.
A side lobe suppression method under a pulse Doppler radar system comprises the following steps:
step 1, establishing a moving target echo signal model, and carrying out two-dimensional matched filtering on a received signal, wherein the specific method comprises the following steps:
the pulse radar is assumed to transmit M coherent pulses with the same waveform, and the pulse length is N; the vector of fast time samples of the transmit pulse is denoted as s ═ s0 s1 … sN-1]T(ii) a Let ymRepresents the m-th pulseFor the range bin of interest L is 0,1,2, …, L-1, the N consecutive samples of the echo signal corresponding to the mth pulse in the ith range bin are represented as:
ym(l)＝[ym(l) ym(l+1) … ym(l+N-1)]T (1)
wherein:
Figure BDA0002285733500000021
x(l，k)＝[x(l，k) x(l-1，k) … x(l-N+1，k)]Tsampling N consecutive range directions for a kth radial velocity, x (l, k) representing the target backscatter coefficients at the kth range bin, the kth Doppler bin; omegakLet T be the Doppler frequency corresponding to the kth radial velocityrωk＝θkAssuming 2 π (K-K/2)/K- π/K ≦ θk< 2 pi (K-K/2)/K + pi/K, where K is the number of doppler units and K is 0,1, …, K-1. n ism(l) For additive noise, considering intra-pulse doppler,
Figure BDA0002285733500000022
wherein T isr、TsPulse repetition interval and sampling interval, respectively;
equation (1) is thus written as:
Figure BDA0002285733500000031
wherein n ism(l)＝[nm(l) nm(l+1) … nm(l+N-1)]T，JnIs an N × N shift matrix and satisfies:
Figure BDA0002285733500000032
when N > N-1, the compound is,
Figure BDA0002285733500000033
the corresponding N consecutive fast time samples of the i-th range profile of the M pulse echoes are:
Y(l)＝[y0(l) y1(l) … yM-1(l)] (5)
two-dimensional matched filtering is carried out on Y (l), and a target estimation result after matched filtering can be obtained
Figure BDA0002285733500000034
Figure BDA0002285733500000035
Wherein
Figure BDA0002285733500000036
N(l)＝[n0(l) n1(l) … nM-1(l)]；
Decomposing formula (6) into:
Figure BDA0002285733500000041
step 2, adding a processing window to the two-dimensional matched filtering result, and utilizing a self-adaptive method to restrain a distance dimension side lobe, wherein the specific method comprises the following steps:
adding a processing window to the two-dimensional matched filtering result, and defining the size as krX 1 filter vector
Figure BDA0002285733500000042
Figure BDA0002285733500000043
Wherein
Figure BDA0002285733500000044
kr1，kr2Respectively matched filtering results
Figure BDA0002285733500000045
Number of distance dimension points before and after, and kr＝kr1+kr2+1；
Figure BDA0002285733500000046
Definition of
Figure BDA0002285733500000047
The interference covariance matrix of (a) is:
Figure BDA0002285733500000048
wherein:
Figure BDA0002285733500000051
constructing a weighted least squares cost function:
Figure BDA0002285733500000052
wherein
Figure BDA0002285733500000053
The minimum value of equation (12) is found for x (l, q) to obtain:
Figure BDA0002285733500000054
using matrix inversion theorem according to equations (10) and (11), we obtain:
Figure BDA0002285733500000055
the estimation result is obtained by bringing equation (14) into equation (13):
Figure BDA0002285733500000056
step 3, iterative operation is carried out on the step 2, distance dimensional interference is restrained, and a target estimation result is obtained
Figure BDA0002285733500000057
The specific method comprises the following steps:
in the first iteration, the interference covariance matrix is initialized by using the matched filtering result, and the estimation result of x (l, q) obtained in the first iteration is obtained according to the calculation of the formulas 10) to 15
Figure BDA0002285733500000058
Based on the estimation result of the first iteration, the calculation of the formulas (10) to (15) is sequentially executed to obtain the estimation result of the second iteration
Figure BDA0002285733500000059
Entering next iteration; and repeating the steps until the iteration termination condition is met, and outputting the estimation result of the last iteration
Figure BDA00022857335000000510
Namely, the distance dimension filtering result is obtained;
step 4, inhibiting Doppler dimension sidelobes, and the specific method is as follows:
the estimation result obtained in the step 3 is used
Figure BDA00022857335000000511
As initial input for Doppler dimension suppression, and is written as
Figure BDA00022857335000000512
To pair
Figure BDA00022857335000000513
Adding a Doppler dimension processing window, scalingMean size kdX 1 filter vector
Figure BDA0002285733500000061
Figure BDA0002285733500000062
Wherein:
Figure BDA0002285733500000063
kd1，kd2respectively the distance dimension filtering results
Figure BDA0002285733500000064
Number of Doppler dimension points before and after, and kd＝kd1+kd2+1，
Figure BDA0002285733500000065
Is an additive noise vector and is ignored;
defining an interference covariance matrix as:
Figure BDA0002285733500000066
the result after Doppler side lobe suppression is obtained:
Figure BDA0002285733500000067
and 5, repeating the step 4 by using an iterative mode to obtain a final estimation result, which specifically comprises the following steps:
at the first iteration, will
Figure BDA0002285733500000068
The covariance matrix R 'is initialized as the initial value of x (l, k) in equation (18)'l，qAfter the substitution of the compound of formula (19),obtaining the estimated value of the first iteration
Figure BDA0002285733500000069
The estimated value is substituted into formula (18) again to obtain a covariance matrix R'l，qThen, the formula (19) is replaced to obtain the estimated value of the second iteration
Figure BDA00022857335000000610
Entering next iteration; and repeating the steps until the iteration termination condition is met, and outputting the estimation result of the last iteration
Figure BDA0002285733500000071
Preferably, the iteration stop condition in step 3 is: when the estimation result is
Figure BDA0002285733500000072
Is smaller than the set value.
Preferably, the iteration stop condition in step 5 is: estimation result
Figure BDA0002285733500000073
Is smaller than the set value.
The invention has the following beneficial effects:
the invention provides a fast side lobe suppression method based on a two-dimensional matched filtering result, aiming at solving the problem of high side lobe of distance-Doppler after two-dimensional matched filtering in a pulse Doppler radar, wherein the method can realize side lobe suppression with lower calculation amount and improve the parameter estimation precision and imaging quality of a target in a multi-target scene by adding a processing window to the two-dimensional matched filtering result and utilizing an iterative adaptive method based on least square to realize side lobe suppression; due to the adoption of windowing processing, the covariance matrix is subjected to dimension reduction processing, the calculation complexity can be reduced, and the calculation amount is further reduced by utilizing the structural relationship among the matrixes.
Drawings
FIG. 1 is a schematic view of a process window.
FIG. 2(a) shows R in the case of distance dimension suppressionl+1，qAnd Rl，qA matrix relation analysis graph;
FIG. 2(b) is a graph showing R in Doppler dimension suppressionl+1，qAnd Rl，qA matrix relation analysis graph;
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
Step 1, establishing a moving target echo signal model, and carrying out two-dimensional matched filtering on a received signal, wherein the specific method comprises the following steps:
assume that a pulse radar transmits M coherent pulses of the same waveform and that the pulse length is N. Then the fast time sample vector of the transmit pulse may be expressed as s ═ s0 s1 … sN-1]T. Let ymRepresenting the echo signal of the mth pulse, then for the range bin of interest L being 0,1,2, …, L-1, the N consecutive samples of the echo signal corresponding to the mth pulse in the mth range bin can be expressed as:
ym(l)＝[ym(l) ym(l+1) … ym(l+N-1)]T (1)
wherein:
Figure BDA0002285733500000081
x(l，k)＝[x(l，k) x(l-1，k) … x(l-N+1，k)]Tx (l, k) represents the target backscatter coefficients at the ith range bin, the kth doppler bin, for consecutive N range direction samples corresponding to the kth radial velocity. OmegakLet T be the Doppler frequency corresponding to the kth radial velocityrωk＝θkIn general, we assume 2 π (K-K/2)/K- π/K ≦ θk< 2 pi (K-K/2)/K + pi/K, where K is the number of doppler units and K is 0,1, …, K-1. n ism(l) For additive noise, considering intra-pulse doppler,
Figure BDA0002285733500000082
wherein T isr、TsRespectively pulse repetition interval and sampling interval.
Equation (1) can thus be written as:
Figure BDA0002285733500000083
wherein n ism(l)＝[nm(l) nm(l+1) … nm(l+N-1)]T，JnIs an N × N shift matrix and satisfies
Figure BDA0002285733500000084
It is noted that when N > N-1,
Figure BDA0002285733500000085
then the corresponding first N fast time samples of the first range image of the M pulse echoes are
Y(l)＝[y0(l) y1(l) … yM-1(l)] (5)
Two-dimensional matched filtering is carried out on Y (l), and a target estimation result after matched filtering can be obtained
Figure BDA0002285733500000095
Figure BDA0002285733500000091
Wherein
Figure BDA0002285733500000092
N(l)＝[n0(l) n1(l) … nM-1(l)]。
From equation (6), the matched filtering result for a given unit
Figure BDA0002285733500000093
Not only x (l, q), but also the interference and noise of the adjacent unit target images. To more clearly express the matched filtering result of the adjacent unit target pair after matched filtering
Figure BDA0002285733500000096
Can be decomposed into
Figure BDA0002285733500000094
The first term on the right of the equation is the expected matched filter result, the second term is the distance-dimensional interference caused by targets with the same velocity in different range bins, the third term is the doppler-dimensional interference caused by targets with different velocities in the same range bin, the fourth term is the interference caused by targets with different velocities in different range bins, and the fifth term is the noise interference. These unwanted interferences can lead to inaccurate target parameter estimation and affect imaging quality. It is therefore desirable to address this problem with side lobe suppression methods.
Step 2, adding a processing window to the two-dimensional matched filtering result, and utilizing a self-adaptive method to restrain a distance dimension side lobe, wherein the specific method comprises the following steps:
adding a processing window to the two-dimensional matched filtering result, and defining the size as krX 1 filter vector
Figure BDA0002285733500000101
Figure BDA0002285733500000102
Wherein
Figure BDA0002285733500000103
kr1，kr2Respectively matched filtering results
Figure BDA0002285733500000104
Number of distance dimension points before and after, and kr＝kr1+kr2+1；
Figure BDA0002285733500000105
Definition of
Figure BDA0002285733500000106
The interference covariance matrix of (a) is:
Figure BDA0002285733500000107
wherein:
Figure BDA0002285733500000108
constructing a weighted least squares cost function:
Figure BDA0002285733500000109
wherein
Figure BDA0002285733500000111
The minimum value of equation (12) is found for x (l, q):
Figure BDA0002285733500000112
from equations (10) and (11), we can obtain, using matrix inversion theorem:
Figure BDA0002285733500000113
then, the estimation result can be obtained by bringing equation (14) into equation (13):
Figure BDA0002285733500000114
obviously, in the formula (13)
Figure BDA0002285733500000115
Can be prepared from
Figure BDA0002285733500000116
Instead, we have found from the above derivation that the computational effort of the proposed algorithm is mainly embodied in the computation of the covariance matrix, vector according to equation (11)
Figure BDA0002285733500000117
And
Figure BDA0002285733500000118
respectively Rl，qAnd Rl+1，q. The relationship between these two matrices is shown in FIG. 2(a), thus for a known Rl，qCalculating Rl+1，qThen we only need to calculate Rl+1，qAnd Rl，qThe non-overlapping portion, i.e., the shaded portion, is sufficient, whereby the amount of calculation can be further reduced.
Step 3, iterative operation is carried out on the step 2, distance dimensional interference is restrained, and a target estimation result is obtained
Figure BDA0002285733500000119
The specific method comprises the following steps:
from the equation (11), the covariance matrix Rl，qIs related to the unknown signal x (l, q), so the algorithm needs to be implemented in an iterative manner, repeating step 2 until convergence, i.e.: in the first iteration, the interference covariance matrix is initialized by using the matched filtering result, and the estimation result of x (l, q) is obtained in the first iteration through calculation according to the formulas 10) to 15
Figure BDA00022857335000001110
Based on the estimation result of the first iteration, the meters of equations (10) to (15) are sequentially executed againCalculating to obtain the estimation result of the second iteration
Figure BDA00022857335000001111
Entering next iteration; and repeating the steps until the iteration termination condition is met, and outputting the estimation result of the last iteration
Figure BDA00022857335000001112
Namely, the distance dimension filtering result is obtained; in the present invention, when the estimation result is obtained
Figure BDA00022857335000001113
When the variation range of (2) is smaller than the set value, the iteration can be stopped.
Step 4, after the above processing, the range dimensional sidelobe of the target is effectively suppressed, and the doppler dimensional sidelobe is suppressed by the same method as follows:
the estimation result obtained in the step 3 is used
Figure BDA0002285733500000121
As initial input for Doppler dimension suppression, and is written as
Figure BDA0002285733500000122
To pair
Figure BDA0002285733500000123
Adding a Doppler dimension processing window, defining a size of kdX 1 filter vector
Figure BDA0002285733500000124
Figure BDA0002285733500000125
Wherein:
Figure BDA0002285733500000126
kd1，kd2respectively the distance dimension filtering results
Figure BDA0002285733500000127
Number of Doppler dimension points before and after, and kd＝kd1+kd2+1，
Figure BDA0002285733500000128
As additive noise vectors, are negligible.
Defining an interference covariance matrix as:
Figure BDA0002285733500000129
similarly, the result after doppler dimensional sidelobe suppression can be obtained:
Figure BDA00022857335000001210
likewise, matrix R'l，qAnd R'l，q+1The relationship between (A) and (B) is shown in FIG. 2(b), thus for known R'l，qWe need only calculate R'l，q+1The hatched portion of (a) is sufficient.
Step 5, due to covariance matrix R'l，qIs related to the unknown signal x (l, q), so it needs to be realized by repeating step 4 in an iterative manner until convergence and a final estimation result is obtained, namely:
at the first iteration, will
Figure BDA0002285733500000131
The covariance matrix R 'is initialized as the initial value of x (l, k) in equation (18)'l，qAfter the formula (19) is replaced, the estimated value of the first iteration is obtained
Figure BDA0002285733500000132
The estimated value is substituted into formula (18) again to obtain a covariance matrix R'l，qThen substituted into formula(19) To obtain the estimated value of the second iteration
Figure BDA0002285733500000133
Entering next iteration; and repeating the steps until the iteration termination condition is met, and outputting the estimation result of the last iteration
Figure BDA0002285733500000134
In the present invention, when the estimation result is obtained
Figure BDA0002285733500000135
When the variation range of (2) is smaller than the set value, the iteration can be stopped.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (3)

1. A sidelobe suppression method under a pulse Doppler radar system is characterized by comprising the following steps:
step 1, establishing a moving target echo signal model, and carrying out two-dimensional matched filtering on a received signal, wherein the specific method comprises the following steps:
the pulse Doppler radar is assumed to transmit M coherent pulses with the same waveform, and the pulse length is N; the vector of fast time samples of the transmit pulse is denoted as s ═ s0 s1 ... sN-1]T(ii) a Let ymThe echo signal representing the mth pulse, where L is 0,1,2, …, L-1 for the mth range bin of interest, and N consecutive samples of the echo signal corresponding to the mth pulse in the mth range bin are represented as:
ym(l)＝[ym(l) ym(l+1) … ym(l+N-1)]T (1)
wherein:
Figure FDA0003057556360000011
x(l,k)＝[x(l,k) x(l-1,k) … x(l-N+1,k)]Tsampling N consecutive range directions for a kth radial velocity, x (l, k) representing the target backscatter coefficients at the kth range bin, the kth Doppler bin; omegakLet T be the Doppler frequency corresponding to the kth radial velocityrωk＝θkAssuming 2 π (K-K/2)/K- π/K ≦ θk< 2 pi (K-K/2) K + pi/K, where K is the number of doppler units, K is 0,1, …, K-1; n ism(l) For additive noise, considering intra-pulse doppler,
Figure FDA0003057556360000012
wherein T isr、TsPulse repetition interval and sampling interval, respectively;
equation (1) is thus written as:
Figure FDA0003057556360000013
wherein n ism(l)＝[nm(l) nm(l+1) … nm(l+N-1)]T，JnIs an N × N shift matrix and satisfies:
Figure FDA0003057556360000021
when N > N-1, the compound is,
Figure FDA0003057556360000022
the corresponding N consecutive fast time samples of the i-th range profile of the M pulse echoes are:
Y(l)＝[y0(l) y1(l) … yM-1(l)] (5)
two-dimensional matched filtering is carried out on Y (l), and a target estimation result after matched filtering can be obtained
Figure FDA0003057556360000023
Figure FDA0003057556360000024
Wherein
Figure FDA0003057556360000025
N(l)＝[n0(l) n1(l) … nM-1(l)]；
Decomposing formula (6) into:
Figure FDA0003057556360000026
step 2, adding a processing window to the two-dimensional matched filtering result, and utilizing a self-adaptive method to restrain a distance dimension side lobe, wherein the specific method comprises the following steps:
adding a processing window to the two-dimensional matched filtering result, and defining the size as krX 1 filter vector
Figure FDA0003057556360000031
Figure FDA0003057556360000032
Wherein
Figure FDA0003057556360000033
kr1，kr2Respectively matched filtering results
Figure FDA0003057556360000034
Number of distance dimension points before and after, and kr＝kr1+kr2+1；
Figure FDA0003057556360000035
Definition of
Figure FDA0003057556360000036
The interference covariance matrix of (a) is:
Figure FDA0003057556360000037
wherein:
Figure FDA0003057556360000038
constructing a weighted least squares cost function:
Figure FDA0003057556360000039
wherein
Figure FDA00030575563600000310
The minimum value of equation (12) is found for x (l, q) to obtain:
Figure FDA0003057556360000041
using matrix inversion theorem according to equations (10) and (11), we obtain:
Figure FDA0003057556360000042
the estimation result is obtained by bringing equation (14) into equation (13):
Figure FDA0003057556360000043
step 3, iterative operation is carried out on the step 2, distance dimensional interference is restrained, and a target estimation result is obtained
Figure FDA0003057556360000044
The specific method comprises the following steps:
in the first iteration, the interference covariance matrix is initialized by using the matched filtering result, and the estimation result of x (l, q) obtained in the first iteration is obtained according to the calculation of the formulas (10) to (15)
Figure FDA0003057556360000045
Based on the estimation result of the first iteration, the calculation of the formulas (10) to (15) is sequentially executed to obtain the estimation result of the second iteration
Figure FDA0003057556360000046
Entering next iteration; and repeating the steps until the iteration termination condition is met, and outputting the estimation result of the last iteration
Figure FDA0003057556360000047
Namely, the distance dimension filtering result is obtained;
step 4, inhibiting Doppler dimension sidelobes, and the specific method is as follows:
the estimation result obtained in the step 3 is used
Figure FDA0003057556360000048
As initial input for Doppler dimension suppression, and is written as
Figure FDA0003057556360000049
To pair
Figure FDA00030575563600000410
Adding a Doppler dimension processing window, defining a size of kdX 1 filter vector
Figure FDA00030575563600000411
Figure FDA00030575563600000412
Wherein:
Figure FDA0003057556360000051
kd1，kd2respectively the distance dimension filtering results
Figure FDA0003057556360000052
Number of Doppler dimension points before and after, and kd＝kd1+kd2+1，
Figure FDA0003057556360000053
Is an additive noise vector and is ignored;
defining an interference covariance matrix as:
Figure FDA0003057556360000054
the result after Doppler side lobe suppression is obtained:
Figure FDA0003057556360000055
and 5, repeating the step 4 by using an iterative mode to obtain a final estimation result, which specifically comprises the following steps:
at the first iteration, will
Figure FDA0003057556360000056
The covariance matrix R 'is initialized as the initial value of x (l, k) in equation (18)'l,qAfter the formula (19) is replaced, the estimated value of the first iteration is obtained
Figure FDA0003057556360000057
The estimated value is substituted into formula (18) again to obtain a covariance matrix R'l,qThen, the formula (19) is replaced to obtain the estimated value of the second iteration
Figure FDA0003057556360000058
Entering next iteration; and repeating the steps until the iteration termination condition is met, and outputting the estimation result of the last iteration
Figure FDA0003057556360000059
2. The sidelobe suppression method under the pulse doppler radar regime according to claim 1, wherein the iteration termination condition in step 3 is: when the estimation result is
Figure FDA00030575563600000510
Is smaller than the set value.
3. The sidelobe suppression method under the pulse doppler radar regime according to claim 1, wherein the iteration termination condition in step 5 is: estimation result
Figure FDA00030575563600000511
Is smaller than the set value.
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